It is because from the Federation's perspective it was an inconsequential border skirmish with an insignificant minor power. Sure it deeply affected those who were personally involved, but to the Federation as a whole it wouldn't have really much mattered.
WAR
noun
- 1.
a state of armed conflict between different nations or states or different groups within a nation or state.
"Japan declared war on Germany"
synonyms: conflict, warfare, combat, fighting, struggle, armed conflict, action, military action, bloodshed, contest, tussle; More
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skir·mish
Dictionary result for skirmish
/ˈskərmiSH/
noun
- 1.
an episode of irregular or unpremeditated fighting, especially between small or outlying parts of armies or fleets.
synonyms: fight, battle, clash, conflict, encounter, confrontation, engagement, fray, contest, combat, tussle, scrimmage, fracas, affray, melee;
archaicrencounter
"the unit was caught up in several skirmishes"
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A skirmish is a small scale type of action or engagement that happens during a state of war.
Therefore, by definition, the Cardassian War was not a skirmish.
"The Wounded" opens with:
Captain's log, stardate 44429.6. We are on a mapping survey near the Cardassian sector. It has been nearly a year since a peace treaty ended the long conflict between the Federation and Cardassia.
Clearly the Cardassian War was a war, a long conflict lasting for years. As a border conflict it might have been a low intensity conflict. But by definition it was not a a single skirmish. One single "accidental" border skirmish could have been smoothed over with an apology, and a peace treaty would not have been needed.
But on the other hand the Cardassian War could have been a very minor border conflict from the point of view of the Federation as a whole.
From the Federation's point of view it might have been similar to Indian Wars in the American west.
Even the largest western Indian nations were outnumbered a thousand to one by Americans, and even all the western Indians together were still outnumbered hundreds to one by Americans. Most of the combats were fought by (19th century sized) companies or subdivisions of them, with examples of commands consisting of (19th century sized) regiments being exceptional, and commands consisting of (19th century sized) brigades were much rarer, and I have heard of only two commands consisting of (19th century sized) divisions. Forces of hostile Indians were in the same size range.
So for most Americans the Indian Wars meant nothing more than occasional newspaper headlines about exciting but far off events.
Similarly, the Roman empire at its height was thousands of times as large, as populous, and as powerful as many of the small states on its borders, so a border war with one of those small states on the border would be a minor event from the viewpoint of the empire as a whole.
And the border war with the Cardassians may have been on the same scale relative to the Federation. Except that such a theory makes it hard to see how the Cardassians could have been an important ally for the Dominion.